NAG Toolbox: nag_lapack_zheevx (f08fp)

Purpose

nag_lapack_zheevx (f08fp) computes selected eigenvalues and, optionally, eigenvectors of a complex nn by nn Hermitian matrix AA. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.

Syntax

Description

The Hermitian matrix AA is first reduced to real tridiagonal form, using unitary similarity transformations. The required eigenvalues and eigenvectors are then computed from the tridiagonal matrix; the method used depends upon whether all, or selected, eigenvalues and eigenvectors are required.

where εε is the machine precision. If abstol is less than or equal to zero, then ε‖T‖1ε‖T‖1 will be used in its place, where TT is the tridiagonal matrix obtained by reducing AA to tridiagonal form. Eigenvalues will be computed most accurately when abstol is set to twice the underflow threshold 2 × x02am()2×x02am(), not zero. If this function returns with INFO > 0INFO>0, indicating that some eigenvectors did not converge, try setting abstol to 2 × x02am()2×x02am(). See Demmel and Kahan (1990).

Optional Input Parameters

1:
n – int64int32nag_int scalar

Default:
The first dimension of the array a and the second dimension of the array a. (An error is raised if these dimensions are not equal.)

if INFO = 0INFO=0, the first m columns of ZZ contain the orthonormal eigenvectors of the matrix AA corresponding to the selected eigenvalues, with the iith column of ZZ holding the eigenvector associated with w(i)wi;

if an eigenvector fails to converge (INFO > 0INFO>0), then that column of ZZ contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in jfail.

It is possible that info refers to a parameter that is omitted from the MATLAB interface. This usually indicates that an error in one of the other input parameters has caused an incorrect value to be inferred.